Probably it might take a little longer, because less use of planes and less pressure because no economic incentives and better work conditions. Also here are some ideas for a more solar punk postal system:
I think there might a less individualized approach to receiving letters... In my building we have 40 living units and everyone has their own letterbox. In a more community based approach to this there might be just one letter box to save resources(material and time to find the right letter box) or there might be rotating responsibility to get the letters from the local post office.
Changing the responsibility of the last mile transport from a specialized worker to some kind of community task seems pretty fun to me, like communities could decide how often / which time of the day / how to transport and hand out the letters. Also the post office would become a kind of hub where every group of people living in the area would meet each other regularly and maybe that would also lead to interesting things.